Data Unit (Lossy vs Lossless, Binary, Overflow, Roundoff)

A certain programming language uses 4-bit binary sequences to represent nonnegative integers. For example, the binary sequence 0101 represents the corresponding decimal value 5. Using this programming language, a programmer attempts to add the decimal values 14 and 15 and assign the sum to the variable total. Which of the following best describes the result of this operation?

• The correct sum of 29 will be assigned to the variable total.

• An overflow error will occur because 4 bits is not large enough to represent either of the values 14 or 15.

• An overflow error will occur because 4 bits is not large enough to represent 29, the sum of 14 and 15.

• A round-off error will occur because the decimal values 14 and 15 are represented as approximations due to the fixed number of bits used to represent numbers.

Which of the following is an advantage of a lossless compression algorithm over a lossy compression algorithm?

• A lossless compression algorithm can guarantee that compressed information is kept secure, while a lossy compression algorithm cannot.

• A lossless compression algorithm can guarantee reconstruction of original data, while a lossy compression algorithm cannot.

• A lossless compression algorithm typically allows for faster transmission speeds than does a lossy compression algorithm.

• A lossless compression algorithm typically provides a greater reduction in the number of bits stored or transmitted than does a lossy compression algorithm.

ASCII is a character-encoding scheme that uses 7 bits to represent each character. The decimal (base 10) values 65 through 90 represent the capital letters A through Z, as shown in the table below.

What ASCII character is represented by the binary (base 2) number 1001010 ?

• H

• I

• J

• K

An online store uses 6-bit binary sequences to identify each unique item for sale. The store plans to increase the number of items it sells and is considering using 7-bit binary sequences. Which of the following best describes the result of using 7-bit sequences instead of 6-bit sequences?

• 2 more items can be uniquely identified.

• 10 more items can be uniquely identified.

• 2 times as many items can be uniquely identified.

• 10 times as many items can be uniquely identified.

A video game character can face toward one of four directions: north, south, east, and west. Each direction is stored in memory as a sequence of four bits. A new version of the game is created in which the character can face toward one of eight directions, adding northwest, northeast, southwest, and southeast to the original four possibilities. Which of the following statements is true about how the eight directions must be stored in memory?

• Four bits are not enough to store the eight directions. Five bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Eight bits are needed for the new version of the game.

• Four bits are not enough to store the eight directions. Sixteen bits are needed for the new version of the game.

• Four bits are enough to store the eight directions.

When two positive integers are added together, it results in an overflow error. Which of the following best explains why an overflow error occurs?

• The program attempted to perform an operation that is considered an undecidable problem.

• The precision of the result is limited due to the constraints of using a floating-point representation.

• The program can only use a fixed number of bits to represent integers; the computed sum is greater than the maximum representable value.

• The program cannot represent integers; the integers are converted into decimal approximations, leading to rounding errors.

A user wants to save a data file on an online storage site. The user wants to reduce the size of the file, if possible, and wants to be able to completely restore the file to its original version. Which of the following actions best supports the user’s needs?

• Compressing the file using a lossless compression algorithm before uploading it

• Compressing the file using a lossy compression algorithm before uploading it

• Compressing the file using both lossy and lossless compression algorithms before uploading it

• Uploading the original file without using any compression algorithm

The player controls in a particular video game are represented by numbers. The controls and their corresponding binary values are shown in the following table. What control can be represented by the decimal value 25?

• Jump

• Run

• Pause

• Reset

Which of the following is a true statement about data compression?

• Data compression is only useful for files being transmitted over the Internet.

• Regardless of the compression technique used, once a data file is compressed, it cannot be restored to its original state.

• Sending a compressed version of a file ensures that the contents of the file cannot be intercepted by an unauthorized user.

• There are trade-offs involved in choosing a compression technique for storing and transmitting data.

Which of the following are true statements about the data that can be represented using binary sequences?

I. Binary sequences can be used to represent strings of characters.

II. Binary sequences can be used to represent colors.

III. Binary sequences can be used to represent audio recordings.

• I only

• I and II only

• II and III only

• I, II, and III